Think about what the U.S. government would do if a political group laid out a road map for overthrowing President Barack Obama, Maduro said Thursday in an exclusive interview with CNN's Christiane Amanpour.

"What would happen in the United States if a group said they were going to start something in the United States so that President Obama leaves, resigns, to change the constitutional government of the United States?" Maduro said, according to a CNN translation of his remarks."Surely, the state would react, would use all the force that the law gives it to re-establish order and to put those who are against the Constitution where they belong."

Maduro said that a minority group among the opposition is responsible for a "violent plan." That group, he said, has put the opposition in a "dire situation."

"He created a road map to topple the legitimate government," Maduro said. "So now he's in jail and he has to go through justice."

Maduro said he supported Venezuelans' right to protest conditions in the country, which he said were not as bad as was being portrayed. For example, he said, unemployment has dropped from 25% to less than 10% over the past decade and extreme poverty has fallen from about 35% during the 1990s to 6% today.

He made no apologies for continuing work on the goals spearheaded during the reign of his predecessor and lifted from the playbook that guided his mentor, former Cuban President Fidel Castro -- health care and education to all and the eradication of extreme poverty.

Protesters have accused Maduro's government of violence that has claimed some 20 lives during the protests. Government officials have blamed Lopez and other opposition leaders for fueling the violence and not doing enough to stop it.

Maduro said the unrest had not kept him awake at night. "I sleep like a child," he said. "Luckily, I have peace of mind, total peace of mind, and I have it because I know I've been loyal and I'm filling the legacy of this marvelous giant figure who is President Chavez, and it gives me peace of mind, and I do things with honesty to favor my people."

Maduro said Venezuela has fine relations with the people of the United States. He cited trade union workers, artists, intellectuals and members of social movements as examples.

But he acknowledged that relations between Washington and Caracas have been rocky. "There is sufficient evidence of U.S. agencies, of how you have conspired to put an end to this revolution, to destroy President Chavez," he said.

But Maduro held out hope for warmer relations. "We want to have a new type of relation, based on respect, equality among states and the recognition of what we are today," he said.

He said he was confident that his recent appointment of Maximilian Arvelaez as his new ambassador to Washington, a position that's been vacant since 2008, would result in progress. "I'm certain that he will be very helpful to establish new levels of relations," he said.

Washington has appeared far less enthusiastic about closer ties with Venezuela.

A State Department spokeswoman said last month that the United States wants to develop "a more constructive relationship with Venezuela," but noted that wouldn't be easy.

"We've said many months ago that could include an exchange of ambassadors," the spokeswoman, Jen Psaki, told reporters. "But Venezuela also needs to show seriousness for us to be able to move forward. And recent actions, including expelling three of our diplomats, continue to make that difficult."

That tense relationship could change, Maduro said.

Asked what his message was for the United States, the Venezuelan President didn't hesitate.

"My message is respect, dialogue, overcoming the visions that they have about Venezuela. Precisely, I made a decision to designate a new ambassador for the United States," Maduro said. "Don't go into a dead end in relation to Venezuela and Latin America. Our message to everyone in power in the United States is respect Venezuela, respect Latin America, and let's establish new levels of relations."